The Tower of Hanoi Problem with Evildoer Discs

Abstract

This paper deals with a variant of the classical Tower of Hanoi problem with n (  1) discs, of which r discs are evildoers, each of which can be placed directly on top of a smaller disc any number of times. Denoting by E(n, r) the minimum number of moves required to solve the new variant, is given a scheme find the optimality equation satisfied by E(n, r). An explicit form of E(n, r) is then obtained.

A Note on the Tower of Hanoi Problem with Evildoers

“…The problem posed by Chen et al (2007) was taken up by Majumdar (2019) and Majumdar & Islam (2020). Let E(n, r) be the minimum number of moves required to solve the above variant.…”

“…Let E(n, r) be the minimum number of moves required to solve the above variant. Then, an explicit form of E(n, r), due to Majumdar (2019), is given as follows:…”

New variants of the bottleneck tower of Hanoi problems

“…The bottleneck Reve's puzzle was proposed by Majumdar (1996), who gave a scheme to derive the dynamic programming equation for the optimal value function. Based on some localvalue relationships, Majumdar and Halder (1996) presented a recurrence relation to calculate the optimal value function as well as the optimal partition numbers recursively in n.…”